Solve for $x$ and $y$ using elimination. ${-2x-2y = -34}$ ${2x-5y = -15}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-7y = -49$ $\dfrac{-7y}{{-7}} = \dfrac{-49}{{-7}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-2x-2y = -34}\thinspace$ to find $x$ ${-2x - 2}{(7)}{= -34}$ $-2x-14 = -34$ $-2x-14{+14} = -34{+14}$ $-2x = -20$ $\dfrac{-2x}{{-2}} = \dfrac{-20}{{-2}}$ ${x = 10}$ You can also plug ${y = 7}$ into $\thinspace {2x-5y = -15}\thinspace$ and get the same answer for $x$ : ${2x - 5}{(7)}{= -15}$ ${x = 10}$